A new source of seed pairs for Golay sequences of length 2m

In 2007 Jedwab and Parker proposed [10] that the natural viewpoint for a Golay complementary sequence is as a projection of a multi-dimensional Golay array. In 2008 Fiedler, Jedwab and Parker [5] used this viewpoint to show how to construct and enumerate all known 2-phase Golay sequences of length 2, starting from two sources of Golay seed pairs. The first source of seed pairs is the trivial Golay pair of length 1, which gives rise to “standard” Golay sequences; the second source is the set of 512 non-standard “cross-over” 4-phase Golay pairs of length 8, which give rise to non-standard 4-phase Golay sequences of length 2 for each m ≥ 4. Beginning with a single length 5 complex-valued Golay sequence pair, we show how to construct a third source of Golay seed pairs (and only the second known non-trivial source), namely a new set of 5184 non-standard 6-phase Golay sequences of length 16 that form 62208 non-standard ordered Golay pairs. Using the multi-dimensional viewpoint, this new set of Golay seed pairs in turn gives rise to a new infinite family of 6-phase non-standard Golay sequences of length 2 for each m ≥ 4, and a new infinite family of 12-phase non-standard Golay sequences of length 2 for each m ≥ 8. All currently known H-phase Golay sequences of length 2 can be constructed from the three sets of seed pairs.